A mass formula for negacyclic codes of length 2k and some good negacyclic codes over ź4+uź4$\mathbb {Z}_{4}+u\mathbb {Z}_{4}$

In this paper, we study negacyclic codes of length 2k over the ring R=ź4+uź4$R=\mathbb {Z}_{4}+u\mathbb {Z}_{4}$, u2 = 0. We have obtained a mass formula for the number of negacyclic of length 2k over R. We have also determined the number of self-dual negacyclic codes of length 2k over R. This study has been further generalized to negacyclic codes of any even length using discrete Fourier transform approach over R. We have conducted an exhaustive search and obtained some new ź4$\mathbb {Z}_{4}$-linear codes with good parameters.